WASHINGTON -- Some Republicans are starting to have buyer's remorse over their party's insistence that a vote to raise the debt limit be tied to a long-term deficit reduction package.

"Maybe the debt ceiling was the wrong place to pick a fight, as it related to trying to get our country's house in order," Sen. Bob Corker (R-Tenn.) said Thursday. "Maybe that was the wrong place to do it."

Speaking from the Senate floor, Corker said Republicans demanded linking the two issues because the Senate hasn't passed a budget in more than 800 days. "I credit both sides for that," he said. But now, the inability of the White House and Congress to agree to a spending deal -- and ensure a timely debt ceiling increase -- is "helping our great nation go into decline."

For months, House and Senate GOP leaders have vowed not to raise the debt limit without tying the vote to substantial deficit reduction. The White House and Democratic leaders initially protested, citing grave economic consequences of toying with a debt-ceiling hike. But they eventually acquiesced as Republican leaders made it clear they weren't budging.

“To increase the debt limit without simultaneously addressing the drivers of our debt, in defiance of the will of our people, would be monumentally arrogant and massively irresponsible," Speaker John Boehner (R-Ohio) said in May at the Economic Club of New York.

“So let me be as clear as I can be: Without significant spending cuts and reforms to reduce our debt, there will be no debt limit increase. And the cuts should be greater than the accompanying increase in debt authority the president is given," he continued.

Senate Minority Leader Mitch McConnell (R-Ky.) in March threatened that Republicans wouldn't raise the debt limit unless it was tied to a "credible effort" to shrink the nation's overall debt.

"I don't intend to support raising the debt ceiling, and I don't believe any Senate Republicans do, unless we do something important related to spending and debt," McConnell said on "Fox News Sunday."

"It is going to have to carry something with it that the markets, foreign countries and the American people believe is a credible effort to get a handle on spending and the debt effort."

As it stands, the Treasury has estimated that the government will run out of money to pay its bills on August 2. Negotiators still don't have a plan to prevent that from happening. That stark reality is already having real consequences: Moody's warned on Wednesday that the United States may lose its top credit rating if negotiators can't reach agreement soon. Standard & Poor's has reportedly warned lawmakers privately that the firm could also lower its rating of the government's debt if a deal does not materialize soon, according to Reuters.

During his Senate remarks, Corker said the dozen Senators from both parties that he had dinner with on Monday all expressed "tremendous frustration" with the way electoral politics have taken hold in the Senate as a potential debt default looms.

"I won't mention their names, to impugn them in any way," the Tennessee Republican added, referring to his dinner company. But all agreed that "most Senators in this body are nothing but two-bit pawns ... as a political fight is under way, basically, to lay out the groundwork, if you will, for 2012 elections."